The loss however is augmented by a penalty which forces \(z_1\)  and \(z_2\)  into identity and non-identity factors using two auxiliary networks: a pose network \(P\)  which, operating on a face, returns the 3-angle pose position of the face [1]}, and the ArcFace face embedding network \(F\)  [2]} which returns a face identity embedding in \(\mathbb {R}^{512}\) . Designating the images as \(I_0\)  for anchor, \(I_+\)  for fixed identity and \(I_-\)  for different identity images, the new losses which we introduce to the existing GAN losses are:
\(\begin{split}L_P^- = \Vert {P(I_0) - P(I_-)}\Vert ^2, &\:L_P^+ = -\Vert {P(I_0) - P(I_+)}\Vert ^2 \\L_F^- = -\arccos {(F(I_0) \cdot F(I_+))}, &\:L_F^+ = \arccos {(F(I_0) \cdot F(I_-))}.\end{split}\) 
